Geodesic
Orthogonal Solutions for a Hyperbolic System
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130

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We consider the hyperbolic system $$ \begin{cases} u_t=a\nabla v+f_1(u,н)\\ v_t=a\nabla u+f_2(u,н)\\ u(0,x)=\xi(x)\\ v(0,x)=\eta(x), \end{cases} $$ and we are looking for necessary and sufficient conditions on the forcing terms $f_i$, $i=1,2$, in order that the semigroup solutions, $u$ and $н$, starting from orthogonal data $\xi,\eta\in L^2(\mathbb R^n)$, remain orthogonal on $\mathbb R_+$. 
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     author = {Ovidiu C\^arj\u{a} and Mihai Necula and Ioan I. Vrabie},
     title = {Orthogonal {Solutions} for a {Hyperbolic} {System}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {125--130},
     publisher = {mathdoc},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2008_1_a6/}
}
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Ovidiu Cârjă; Mihai Necula; Ioan I. Vrabie. Orthogonal Solutions for a Hyperbolic System. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 125-130. http://geodesic.mathdoc.fr/item/BASM_2008_1_a6/